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% Title 
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%\bigskip

%\title{Simulated aerosol water uptake in global aerosol models and its impact on aerosol direct and indirect effect}
\title{Uncertainties in the simulated aerosol water uptake in ECHAM5-HAM2: 
       impact on aerosol direct and indirect effect}
%\title{Notes on aerosol water uptake and its treatment in global aerosol models} 
%\title{On the parameterization of aerosol water-uptake in global aerosol models} 

\author[1]{K.~Zhang}
%\author[1]{H.~Wan}
%\author[2]{D.~O'Donnell}
%\author[1]{X.~Liu}
%\author[2]{J.~Feichter}

\affil[1]{Pacific Northwest National Laboratory, Richland, WA, USA}
%\affil[2]{Max Planck Institute for Meteorology, Hamburg, Germany}

\runningtitle{Aerosol wateruptake in GCMs}
\runningauthor{Zhang et al.}

\correspondence{K.~Zhang (kai.zhang@pnnl.gov)}

%\received{01 July 2010}
%\accepted{31 December 2010}
%\published{21 Jan 2011}

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% Abstract 
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\begin{abstract}
Water uptake by aerosol particles plays a crucial role in determining the wet-size distribution and 
optical properties of aerosol particles, thus has a direct influence on the magnitude of the aerosol 
direct and indirect effects. 
We have performed various sensitivity simulations with the global aerosol-climate ECHAM-HAM 
to quantify the uncertainty in 
the simulated aerosol water uptake. Results show that the dominant factors for global total aerosol 
water burden are the RH ceiling due to high non-linearity at RH$>$95\% and the simulated sea salt 
loading. The use of clear-sky RH (instead of grid-box mean) reduces the global total aerosol 
water burden by 6\%, suggesting the importance of sub-grid variability. With the kappa-Koehler-theory 
based method, the simulated global total aerosol water burden increases rapidly and quasi-linearly 
with enhanced kappa value of sea salt aerosols, which reflects the dominant role of sea salt aerosols in 
water uptake. The impact of water uptake perturbation on direct and indirect forcing estimates 
will also be discussed. These findings suggest that a detailed model inter-comparison of aerosol 
water uptake will be a useful exercise for the global modelling community. 
\end{abstract}


%----------------------------------------------------------- 
% Introduction  
%----------------------------------------------------------- 
\introduction
\label{sec:intro}

Aerosol water uptake has a major effect on the physical and chemical properties of aerosols. 
Water increases particle size and thus affects its lifetime. The light
scattering and, consequently, the visibility reduction and
direct climate forcing by the aerosol particles depend strongly on
their water content [Ramaswamy, 2001]. The
presence of water changes the partitioning of semi-volatile species
between the gas and aerosol phase and affects the
particle composition [Ansari and Pandis, 2000]. In addition, aerosol
water provides a medium for heterogeneous chemical reactions in the
atmosphere.

Water uptake by aerosol particles plays a crucial role in determining the wet-size distribution and
optical properties of aerosol particles, thus has a direct influence on the magnitude of the aerosol
direct and indirect effects. The water content of aerosols depends on their composition as well as
the ambient relative humidity (RH). To represent the water uptake process in global aerosol
models, critical assumptions are made in the parameterizations, such as the maximum RH
allowed for the water uptake calculation (RH ceiling), the sub-grid variation of RH and
composition, the molality and dissociated fraction or the hygroscopic growth factor (or the kappa
value), and etc. The AeroCom A2 models are showing a wide spread in the simulated global
aerosol water burden (60+-45 Tg, range is 12-102 Tg).

\section{Haywood et al. (2000)}
 
1. more sophisticated treatments of the effects of relative humidity for hygroscopic aerosols

2. The local radiative forcing will depend upon the local atmospheric column burden of a particular 
anthropogenic aerosol species in the atmosphere, the underlying surface reflectance and the 
relative vertical position of the aerosol and cloud, the relative humidity if the aerosol 
is hygroscopic, and the insolation.

3. The maximum hygroscopic growth of the aerosols was restricted to a relative humidity of 90%\. 

4. The treatment of the effects of relative humidity and cloud appear to be particularly 
important in determining the radiative forcing. The studies of Haywood and Ramaswamy [1998], 
Penner et al. [1998], and Grant et al. [1999] produce normalized radiative forcings a 
factor of 2–3 higher than the other studies. Both Haywood and Ramaswamy [1998] and 
Penner et al. [1998] acknowledge that their use of on/off cloud schemes where cloud 
fills an entire grid box once a threshold relative humidity is exceeded may lead to 
strong radiative forcings due to strong nonlinear relative humidity effects.

5. Chuang et al. [1997] use an on/off cloud scheme and report a radiative forcing lower 
than these two studies, but the hygroscopic growth is suppressed above a relative humidity of 90%\. 

6. The use of monthly mean relative humidity fields in some of the calculations 
[e.g., Kiehl and Briegleb, 1993; Myhre et al., 1998] leads to lower radiative forcings, 
as temporal variations in relative humidity and associated nonlinear effects are not 
accounted for. Kiehl et al. [2000] improve the treatment of relative humidity compared 
with Kiehl and Briegleb [1993] and Kiehl and Rodhe [1995] by improving the relative 
humidity dependence of the aerosol optical properties and by using on-line GCM relative 
humidities rather than monthly mean analyses, resulting in a larger normalized radiative 
forcing. Haywood and Ramaswamy’s [1998] GCM study indicates a stronger radiative 
forcing when sulphate resides near the surface because the relative humidity is higher. 
GCM sensitivity studies [Boucher and Anderson, 1995] and column calculations 
[Nemesure et al., 1995] show that the radiative forcing is a strong function of 
relative humidity but relatively insensitive to chemical composition. 

7. Additionally, McInnes et al. [1998] suggest that OC may act to suppress the 
hygroscopic nature of sea salt and sulphate; thus the effect of OC emissions 
may, under certain circumstances, result in a net positive forcing. Thus it is very 
unlikely that the radiative forcing from different species will add linearly. 
Further modeling work where all aerosol types, including natural species, 
are included in chemical transport models is necessary if the effects of 
internal mixing upon the overall radiative forcing are to be assessed on a global scale.


Aerosol water uptake is one of the major
uncertainties in global aerosol modelling.

It depends on local RH and composition.
Large differences for composition and AERH2O in Exp B.
Implications on radiative properties !


\section{Ginoux et al. (2006)}

The effect of hygroscopic growth on the extinction coefficients is considered for 
sulfate and sea salt. Sea salt is assumed to be in a maritime environment with 
a constant relative humidity of 80\%, while sulfate extinction varies with the 
calculated relative humidity from CM2.1 at every time step and grid point. As 
indicated in Table 1, the extinction coefficient of sulfate increases by more 
than a factor of 10 as the relative humidity increases from 80\% to 100\%. 
The hygroscopic growth of sulfate between 30\% and 80\%. RH is obtained using 
the method of Haywood and Ramaswamy, [1998], and between 81\% RH and 100\% from
the approximation formula by Fitzgerald [1975]. The sulfate extinction is 
calculated in CM2.1 by linearly interpolating between precalculated extinctions 
archived for specific RH values in a ‘‘look-up’’ table with a step of 2\% 
between 80 and 98\% and then a step of 1\%. The density of wet particles is 
the volume-weighted density of dry aerosol and water. Organic carbon, black 
carbon and dust particles are assumed to be hydrophobic, and their properties 
are independent of relative humidity.


\section{GISS model: Schmidt et al. (2006)} 

Hygroscopic aerosols (i.e., sulfates, nitrates, sea salt, and organic carbon) 
increase in size as the relative humidity increases, which increases the aerosol 
scattering efficiency and radiative forcing (Boucher and Anderson 1995; 
Nemesure et al. 1995; Tang et al. 1981). This increase in particle size has 
been accurately measured in the laboratory and parametric formulas derived to 
express the particle growth as a function of relative humidity, as well as the 
accompanying change in density and refractive index as the initially solid 
particle dissolves and takes on water (Tang 1996; Tang and Munkelwitz 1991, 
1994; Tang et al. 1981). Typically, a particle remains solid until the relative 
humidity reaches a critical value of deliquescence whereupon it rapidly dissolves 
and increases in size with increasing relative humidity. As relative humidity 
decreases, solute particles follow the equilibrium curve until relative humidity 
falls below the crystallization point, whereupon it rapidly loses its water and 
makes a rapid transition to its dry crystalline state. The dominant effect is a 
strongly nonlinear increase in aerosol optical depth as relative humidity 
increases, particularly for relative humidities above 0.9. However, the extinction 
efficiency of a hygroscopic aerosol may either increase or decrease with relative 
humidity, depending on the effective radius of the dry seed size. Based on these 
laboratory measurements, hygroscopic aerosol radiative properties depend explicitly 
on the local relative humidity and fully include the effects of changing refractive 
inded and droplet size on the aerosol Mie scattering properties.

We parameterize this in terms of an external mixture of the dry aerosol and a 
pure water aerosol of appropriate size with the sizes set to reproduce precisely 
the extinction efficiency and asymmetry parameters of the solute aerosol at the 
laboratory wavelength of 633 nm. We have found that the spectral dependence of 
aerosol radiative parameters is retained by the external mixture with excellent 
accuracy. Look-up tables of Mie scattering coefficients are tabulated for 
relative humidities ranging from 0 to 0.999 separately for each aerosol type 
with dry aerosol seed sizes set at model initialization within the range of 
0.1- to 10-μm effective radius.

The evaluation of the resulting aerosol optical thickness is shown in Fig. 2. 
We compare 1990 conditions (the latest period for which emissions were available) 
to the mean Moderate Resolution Imaging Spectroradiometer (MODIS) results from 
2001–03. This comparison is principally an evaluation of the (fixed) aerosol 
mass field and mean relative humidity in the model. Clear-sky values are the 
most appropriate comparison to the satellite observations, while total-sky 
values are significantly higher (due to the correlation of clouds with higher 
relative humidity). The amounts of all of these aerosols are moderately less 
in 1979 than in 1990, the global mean clear-sky aerosol optical depth at 550 
nm being 0.13 in 1979 compared with 0.14 in 1990. The 1979 values are used 
in the model simulations described here.

\section{CAM5: Liu et al. (2012)} 

Water uptake is based on the equilibrium Koehler theory (Ghan and Zaveri, 2007)
using the relative humidity and the volume-mean hygroscopicity for each mode to
diagnose the wet volume-mean radius of the mode from the dry volume-mean radius. The
hygroscopity of each component is listed in Table S3. The hygroscopicities here are
equivalent to the κ parameters of Petters and Kreidenweis (2007). The hygroscopicities
for sea salt, sulfate, ammonium, and SOA are from Petters and Kreidenweis (2007). The
hygroscopicity for BC is set to be zero to represent its hydrophobic nature. Note that the
measured hygroscopicity of dust varies widely, from 0.03 to 0.26 (Koehler et al., 2009),
and a value of 0.068 is used in this study. The measured hygroscopicity of POM can vary
from 0.0 for fossil fuel source to 0.06-0.30 for biomass burning source (Liu and Wang,
2010). We used a value of 0.1 for the hygroscopicity of POM in the standard CAM5, but
investigated the sensitivity in section 5 to a smaller value of 0.0 to reflect the
hydrophobic nature of POM from fossil fuel combustion.

\section{Ghan BAMS review: Aerosol properties and proceses} 

With increasing relative humidity particles may accrete water vapor by 
deliquescence and further hygroscopic growth; with decreasing relative 
humidity water is lost and ultimately particles may effloresce to the 
dry state. The uptake of water increases particle size, affecting also 
the particle optical properties.

\begin{itemize}
\item For external mixtures only; no hysteresis in most models; equilibrium
\item Internal and external; hysteresis treated
\item Kinetic effects
\end{itemize}

\begin{itemize}
\item Hygroscopicity Prescribed 
\item Volume average 
\item Thermodynamic equilibrium
\end{itemize}

Although treating internal mixing can 
reduce the number of aerosol types, it complicates the 
representation of optical properties, hygroscopicity, 
and CCN activity because, as is the case with actual 
ambient aerosol particles, those properties depend 
on the now-variable composition. Fifth-generation 
models will accommodate internal mixing by using 
mixing rules for refractive index and hygroscopicity 
pertinent to particle growth with relative humidity 
and CCN activity

Uptake of water by particles will be represented 
in terms of the bulk hygroscopicity using Köhler 
theory, with explicit treatment of hysteresis so that 
dry and hydrated aerosol states are distinguished.

Hygroscopic growth H-TDMA: Radar and McMurry (1986), Gasparini et al. (2006b)


\section{TM4: Henzing et al. (2006)} 

Another possible source of uncertainty is the growth of particles
with increasing humidity. For the water uptake of
sea salt particles we applied a relation provided by Gerber
(1985). In our model sea salt is externally mixed with other
aerosol particles. Applying the Gerber relation implicitly assumes
that the composition of our sea salt resembles that of
the Navy Aerosol Model (NAM). In reality, sea salt particles
may act as a substrate for heterogeneous chemistry and
will therefore be internally mixed to some extent (Dentener
and Crutzen, 1993). Internal mixing of sea salt particles with
continental pollution and organic compounds reduces their
hygroscopic growth rate (Swietlicki, 2000; Randles et al.,
2004). For below-cloud scavenging this may become important
for aerosol particles with radii around 1 or 2μm where
the differential scavenging coefficient grows very rapidly
with increasing aerosol particle size. Keeping track of internal
mixtures combined with online particle humidity growth
calculations is not foreseen in our model in the near future,
but it is in principle possible. A related issue is the accuracy
of the relative humidity itself, especially at high relative
humidity. At the coarse resolution used here (60×4) a
single, using only an average, value of the relative humidity
in each cell is a poor representation of the spatial variability
of relative humidity. The large changes in relative humidity
fields that are experienced between successive meteo
updates, especially in situations with precipitation, indicates
that the model neither represents temporal variability well.
Moreover relative humidity may not be accurately predicted
below precipitating clouds. The importance of uncertainties
related to relative humidity may be best demonstrated with
an example: The aerosol mass (including associated water)
of a sea salt particle with dry radius 1μm will be underestimated
by a factor 2 if the ambient relative humidity of 90\% is
underestimated at 80\%, the corresponding underestimate in
the differential scavenging coefficient is more than a factor
of 20.


\section{Notes on the k-Koehler theory}

A third point regards the handling of mixtures of solutes. Most thermodynamic models
assume the applicability of the ZSR relation, which states that water contents of binary
solutions can be added to estimate the water content of the mixture. Certainly the
single-salt parameterizations proposed here could be computed individually and then
the water contents added in the same way. The unique advantage of the PK2007
parameterization arises because the same functional dependence on a\_w is used for
all solutes, and then it can be shown that the ZSR assumption is equivalent to volume
weighting the kappas of the mixture components one performing ONE calculation for
the mixed-solute water content.

Again, as with any parameterization, there is a tradeoff between accuracy and computational 
efficiency. The PK2007 parameterization is very simple and so far appears
to work well for water contents at high water activities, such as those accessed during
droplet nucleation. However, it is poor in the subsaturated regime for sodium salts, and
certainly should not be applied under those conditions without corrections.

\section{Aerosol hygroscopicity in Korea: \citet{kim:2011} } 

Hygroscopicity at ∼90\% relative humidity (RH) were measured
at a background monitoring site at Gosan, Jeju Island,
south of the Korean Peninsula in August 2006, April to
May 2007 and August to October 2008

Most of the aerosols were internally mixed and no notable
differences in hygroscopicity were found between the days
of strong pollution inﬂuence and the non-pollution days for
both islands.


\section{Bates et al. (2006)}

Because the soluble components take up water at relative humidity (RH) below 100\%,
water is often a major constituent of aerosol particulate matter. The amount of 
condensed-phase water present in the aerosol increases as the RH increases and 
changes the scattering properties of the aerosol (Tang, 1996; Carrico et al., 2003). 
This uptake of water influences the scattering coefficient mainly through size and 
is partially offset by changes in refractive index. Additionally, some insoluble 
species like soot or dust may have their light scattering and absorbing properties 
substantially increased when coated by or mixed with soluble species 
(Chylek et al., 1995; Fuller et al., 1999; Mishchenko et al., 2004). Consequently, 
the size dependent state of mixing of the aerosol is needed to properly relate 
ambient radiative properties to the composition and microphysical structure of 
the aerosol and the associated optical properties of this aerosol.

Recent improvements in aerosol sampling and analysis techniques have yielded a 
growing body of evidence that primary sea spray particles frequently contain 
organic carbon (Middlebrook et al., 1998; Allan et al., 2004). Recently it has 
been argued from bulk aerosol analysis that over the biologically productive 
North Atlantic Ocean, organic carbon could comprise more than 50\% of the 
sub-micrometer mass (O’Dowd et al., 2004); however, in supermicrometer sea spray 
aerosol the organic mass is a few percent at most (Lewis and Schwartz, 2004).

In the study by O'Dowd et al. (2004), the majority of the organic matter was 
present as non-water soluble organic carbon, suggesting that the water 
uptake and hygroscopic growth factor of sub-micrometer sea-spray enriched in 
organic matter would be substantially less than that for inorganic sea-spray. 
The significance of internally mixed organic carbon upon the hygroscopic 
properties of the sea-salt aerosol remains unclear. Common terpenes 
evidently exert no effect (Cruz and Pandis, 2000), whereas some other organic 
carbon compounds result in suppression of the rate or extent of hygroscopic 
growth (Wise et al., 2003). The latter is shown also in model calculations 
(Ming and Russell, 2001; Randles et al., 2004). However for the coarse mode 
any such effects are assumed here to be small.

\section{John Seinfield's presentation}

\begin{itemize}
\item Researchers have chosen cutoff arbitrarily 
\item Untested RH distributions in GCMs 
\item Representing nonlinear water uptake with grid cell average RH 
\item Subgrid correlations between clouds, RH, and aerosols 
\end{itemize}

\section{Coating and water uptake}

Historically, much of the interest in organics has focused on
the inhibition of CCN activation in cloud by surface-active
organics. Recently, Hansson et al. (1998) found that thick
coatings of either of two insoluble high molecular weight
organics (50 to 100\% by mass of tetracosane or of lauric acid)
reduced the hygroscopic growth factor for particles of NaCl. On
the other hand, studies by Shulman et al. (1996), Cruz and Pandis
(1998), and Virkkula et al. (1999) suggest that coatings of organic
acids do not necessarily inhibit the effect of the other species on
the condensation of water. The ability of the hydrophobic coating
to form a complete barrier to the water vapour is a critical aspect
of this issue. It is unlikely that such coatings are common in the
atmosphere.


The hygroscopic GF of a mixture (GFmixed ) can be estimated from the GFs of the pure components and their
respective volume fractions, , with the ZSR relation (Gysel et al., 2004; Stokes and Robinson, 1966). 

The summation goes over all compounds present in the particles. The model assumes spherical particles, ideal
mixing behavior (i.e. no volume change upon mixing) and independent water uptake of the organic and inorganic
components. 

\section{ US climate aerosol report }

Furthermore, aerosol particle size can grow in the atmosphere because 
the ambient water vapor can condense on the aerosol particles. 
This “swelling” process, called hygroscopic growth, is most commonly 
parameterized in the models as a function of relative humidity.

Processes that determine aerosol size distributions, hygroscopic growth, 
mixing state, as well as CCN concentrations, however, are inadequately 
represented in most of the global models. 

Hygroscopicity the relative ability of a substance (as an aerosol) to absorb 
water vapor from its surroundings and ultimately dissolve. Frequently reported 
as ratio of some property of particle or of particulate phase of an aerosol 
(e.g., diameter, mean diameter) as function of relative humidity to that 
at low relative humidity.

\section{ \citet{saxena:1995} }

The optical and chemical properties of atmospheric particles and their ability 
to act as cloud condensation nuclei (CCN) depend strongly upon their affinity 
for water. Laboratory experiments have shown that water soluble substances 
such as ammonium sulfate, ammonium nitrate, and sodium chloride, which are 
major inorganic components of atmospheric particles, absorb water in an 
amount proportional to water vapor pressure.


\section{ \citet{adams:1999} }

At thermodynamic equilibrium, the amount of water contained in an aerosol particle 
depends on temperature, relative humidity, and composition [Seinfeld and Pandis, 1998]. 
For example at 298K and 80\% relative humidity the volume of an aqueous solution of 
sulfuric acid is about 5.5 times greater than its volume at 0\% relative humidity, 
where as the volume of ammonium bi-sulfate particles is only 3.5 times greater. 
If metastable equilibria are considered, water uptake also depends on the history of 
the particle. The reason the particle's history plays a role in water uptake is 
because of the hysteresis effect in which the relative humidity required for a 
single-component dry solid particle to deliquesce is higher than the relative 
humidity at which an aqueous droplet crystallizes. The deliquescence and crystallization
relative humidity depend, in turn, on particle composition. An ammonium sulfate particle 
cystallizes at 40\% relative humidity, while ammonium bisulfate retains water to much 
lower relative humidities. For multicomponet mixtures the deliquescence and crytallization
behavior is even more complex. Whereas the size a particle attains via uptake of 
water is influenced, as described above, by its composition, its refractive index
is also determined by composition. Sulfuric acid is more hygroscopic than ammonium 
bisulfate or ammonium sulfate, but ammonium sulfate has the highest refactive index
of the three. The overall climate forcing efficiency of sulfate aerosol increases
with both water uptake and refractive index, so that the higher hygroscopicity of 
sulfuric acid is partly compensated by its lower refractive index and vice versa.   


\section{ \citet{chin:2000} }

Table 3 shows the growth factors of particle radius r/rdry for different aerosol 
types at ambient RH, based on the GADS data and the database compiled by 
d'Almeida et al (1991). The re/re,dryvalues in Table 3 are within the previously measured range for

\section{ Chin et al.: Multi-year global aerosol distributions from MODIS (and MISR) and GOCART}
While satellite data (from passive sensors) have been used to constrain models to improve 
their simulations of AOT, their provide little constraints on 3 major quantities that 
diversify the modeling community (e.g. AEROCOM results):
  Vertical distributions
  Aerosol composition
  Aerosol hygroscopic property (water uptake)


\section{ \citet{bian:2009} }

We find that, on a global average, the AOT calculated using RH at a 1×1.25 
horizontal resolution is 11\% higher than that using RH at a 2×2.5 resolution, 
and the corresponding DRE at the top of the atmosphere is 8–9\% and 15\% 
more negative (i.e., more cooling) for total aerosols and anthropogenic 
aerosol alone, respectively, in the finer spatial resolution case.


\section{ \citet{pahlow:2006} }

An important factor affecting the role aerosols play in climate change is their 
hygroscopicity. The swelling of aerosols due to water vapor uptake will enhance 
their ability to scatter radiation. Numerous studies have investigated the 
relationship between aerosol scattering and relative humidity RH in terms of the 
hygroscopic growth factor f(RH) using humidified nephelometers. 
These have been used for airborne or ground-based determination of the growth 
factor considering a ‘‘dry’’ RH over the range 20\%-40\% and a ‘‘wet’’ RH up 
to 90\% [e.g., Covert et al., 1972; McInnes et al., 1998; Kotchenruther et al., 1999; 
Malm et al., 2003]. Humidified Tandem Differential Mobility Analyzers (HTDMAs) 
allow one to determine aerosol hygroscopicity as a function of particle size, 
usually for RH up to 􏱊90\% [e.g., McMurry and Stolzenburg, 1989;
 Covert and Heintzenberg, 1993; Brechtel and Kreidenweis, 2000]. The 
lidar (light detection and ranging) technique provides the opportunity to investigate 
hygroscopic growth of aerosols beyond this RH range, under ambient atmospheric 
conditions and without perturbing the sampled air. Ferrare et al. [1998] used 
Raman lidar to simultaneously measure aerosol backscatter and RH in a study 
that demonstrated the ability of lidar to measure f(RH)b (where b denotes backscatter). 
Wulfmeyer and Feingold [2000] used differential absorption lidar to measure f(RH)b 
in the regime of high RH up to 􏱊98.5\%. More recently Feingold and Morley [2003]
 (henceforth FM) used elastic backscatter lidar data combined with thermodynamic
assumptions of the mixing state of the atmosphere to determine f(RH)b for RH 
up to 􏱊98.5\%. In this paper we make use of this combined lidar-thermodynamic
 approach to determine backscatter f(RH)b for relative humidities close to 
saturation and for a broad range of atmospheric aerosol conditions.


\section{ \citet{roelofs:2010} }

For selected periods of the month with relatively dry and moist conditions 
discrepancies are approximately −30\% and +15\%, respectively. Discrepancies 
during the dry period are partly caused by inaccurate representation of 
boundary layer (BL) dynamics by the model affecting the simulated AOT. 
The model simulates too strong exchange between the BL and the free troposphere, 
resulting in weaker concentration gradients at the BL top than observed for 
aerosol and humidity, while upward mixing from the surface layers into the 
BL appears to be underestimated. The results indicate that beside aerosol 
sulfate and organics also aerosol ammonium and nitrate significantly contribute 
to aerosol water uptake. The simulated day-to-day variability of AOT follows 
synoptic scale advection of humidity rather than particle concentration. Even 
for relatively dry conditions AOT appears to be strongly influenced by the 
diurnal cycle of RH in the lower boundary layer, further enhanced by uptake 
and release of nitric acid and ammonia by aerosol water.


Other reasons are associated with relative humidity (RH). These are 
the nonlinear swelling of hygroscopic aerosol through water uptake 
especially for RH larger than ∼80\% (Schuster et al., 2006), the 
influence of cloud processing on AOT and Angstro ̈m exponent 
(Roelofs and Kamphuis, 2009), and the influence of RH and its 
sub-grid scale variability (Bian et al., 2009; Jeong et al., 2007).


\section{Notes on ZSR method}
\section{M7 wateruptake}

Equilibrium With the Water Vapor

The particles are assumed to be in equilibrium with water vapor. Only the mixed particles are 
assumed to be hygroscopic, consequently the equilibrium wet radius is only calculated for 
particles in the four mixed modes.

For pure sulfate-water particles new parameterizations for water uptake including the Kelvin 
effect, and particle density (ρ) have been developed. They are based on regression fits to 
solutions of the generalized Kelvin equation [Zeleznik, 1991] for temperatures between 240–330K, 
relative humidity between 0.10 and 95\%, pressures between 50 and 1050hPa and sulfate masses 
between 102 and 1012 molecules:

Equation 6

Equation 7

where S is the relative humidity (0–1), T the absolute temperature, P the pressure in Pascal, 
inline equation the number of sulfate molecules in a particle of average mass for mode j, 
and inline equation the percentage SO4 content by volume of the particle. The constant 
coefficients Kp and Hq are given in Tables 2 and 3, respectively. The R2 coefficients for 
the regression between the new parameterization and the solutions are 0.997 for the 
percentage SO4 content by volume and 0.992 for the particle density. The parameterizations 
have the advantage of not requiring an iterative solution. The comparison with the full 
scheme from Zeleznik [1991] has been done for temperature and relative humidity ranges 
where the full scheme is valid. The parameterizations overestimate the water uptake: 
they predict a larger particle radius from a few percent up to 24\% compared to the full 
scheme; the larger differences are at low temperature and high relative humidity limits 
of the parameterization.

For the mixed Aitken and accumulation particles a similar approach is used when both 
soluble and insoluble compounds are present. BC, OC or dust are not assumed to influence 
the water uptake and the effective soluble mass is used to calculate the equilibrium 
density from equations (6) and (7) and from this the total volume and radius of a 
spherical mixed particle. It must be mentioned that organic carbon may change the 
hygroscopic properties of inorganic aerosols [Hansson et al., 1990; Virkkula et al., 1999; 
Tervahattu et al., 2002; Decesari et al., 2003], If sea salt is present in either the 
accumulation or coarse mode, then total ion dissociation is assumed. 
The ZSR method [Zdanovskii, 1948; Stokes and Robinson, 1966] is used to calculate the 
amount of water attached to the particle as well as parameters from Jacobson et al. [1996] 
for the calculation of molalities. At relative humidity larger than 45\% the salts are 
considered dissolved. This value corresponds to the crystallization point for NaCl. 
In fact particles generated from the sea surface undergo evaporation, and below the 
deliquescence point (75.3\% for NaCl) they are in a supersaturated state, and become 
dry only when relative humidity decreases below 42\% [Shaw and Rood, 1990].

This scheme was compared to AIM (aerosol inorganics model) [Carslaw et al., 1995; 
Clegg et al., 1998a, 1998b], which calculates the thermodynamic properties of aerosol 
inorganic constituents (AIM can be run at the European AIM server at http://www.uea.ac.uk) 
for the system nitrate/sodium/sulfate/nitrate/chloride/water at 298.15 K. The testing was 
made on the amount of liquid water for various SO4, Na and Cl concentrations. For relative 
humidity above 75\% M7 predicts somewhat less uptake of water (up to 12\%). For relative 
humidity between 45 and 75\% the overestimation of M7 is around 1–3 orders of magnitude 
due to the fact that the salts are assumed to be fully dissociated and there is no 
formation of solids, whereas in reality particles are in a metastable state.

\section{Aerosol water in MMF \citep{wang:2011b} }

We also noted that aerosol water uptake in the MMF is calculated at each
CRM grid cell with a CRM-scale relative humidity, while aerosol water uptake in CAM5
is calculated at each GCM grid cell with a GCM-grid scale clear-sky relative humidity.
This may be another reason why the MMF simulates the larger clear-sky direct effects,
as previous studies (Haywood et al., 1997) showed that including subgrid variations in
the relative humidity can lead to larger aerosol direct effects because of the nonlinear
dependence of aerosol water uptake on relative humidity.



\section{CMAQ aerosol water (Binkowski et al., 2003)}

The aerosol water content is computed using the ZSR
method [Kim et al., 1993a] from

...

where W is the aerosol liquid water content [kg m-3], M n is
the atmospheric concentration of the nth species [moles
m-3 ], and mn0 is the molality [moles kg-3 ] of the
nth species at a value of water activity (fractional relative
humidity) of aw. The values for molality as a function of
water activity are calculated from laboratory data from
Giauque et al. [1960], Tang and Munkelwitz [1994], and
Nair and Vohra [1975]. The water content of sulfate
aerosols depends strongly upon the ionic ratio of ammo-
nium to sulfate. This ratio varies from zero for sulfuric acid
to 2.0 for ammonium sulfate with intermediate values of 1.0
for ammonium bisulfate, and 1.5 for letovicite. The usual
method of applying the ZSR method would span this range
with a single expression; however, Spann and Richardson
[1985] have shown that this is not correct. They proposed a
modification which resulted in a correction term. A very
similar result is obtained by using the ZSR method between
the ranges of the ionic ratio of sulfuric acid to ammonium
bisulfate, ammonium bisulfate to letovicite, and letovicite to
ammonium sulfate. The binary activity coefficients are
computed using Pitzer’s method and the Bromley method
is used for the multicomponent activity coefficients in the
aqueous solution (see Kim et al. [1993a] for details).


Two  regimes of ammonium to sulfate ionic ratio are
considered. The ammonia deficient regime (in which the
ionic ratio of ammonium to total sulfate ion is less than 2.0)
leads to an acidic aerosol system with very low concen-
trations of dissolved nitrate ion which depend very strongly
on ambient relative humidity. The second regime is one in
which the ammonium to sulfate ratio exceeds 2.0, the
sulfate is completely neutralized, and there is excess ammo-
nia. If there is nitric acid vapor in the system, it will dissolve
in the aqueous particles along with the excess ammonia and
produce abundant nitrate.



%----------------------------------------------------------- model description 
\section{Aerosol water uptake in global aerosol models}
\label{sec:model}


%----------------------------------------------------------- 
% Results 
%----------------------------------------------------------- 
\section{Results}
\label{sec:model}

\subsection{Global burden of aerosol water and dry aerosol} 

\subsection{Aerosol water versus sea salt}  

\subsection{Aerosol water versus sulfate}  

\subsection{Aerosol water mass versus relative humidity}  

\subsection{Aersol water versus AOD}  

\subsection{Aerosol water versus size} 

\subsection{Surface f(RH) and f(RH) aloft?} 

Does aerosol at the surface and aloft respond identically to changes in relative humidity? 

%----------------------------------------------------------- thanks 
\input{thanks}

%----------------------------------------------------------- appendix 
%\input{appendix}

%----------------------------------------------------------- bib 
\bibliographystyle{copernicus}
\bibliography{aw}

%----------------------------------------------------------- tables 
%\input{tables}

%----------------------------------------------------------- plots 
%\input{figures} 


\end{document}


